1. Field of the Invention
The present invention relates to a force sensing element and, more particularly, to a vibrating beam type force sensing element used as a resonant element in a crystal-controlled oscillator. The resonant element is designed to minimize the loss of energy due to a phenomenon known as "end pumping" to maintain a relatively high mechanical Q. The resonant element is also designed to be virtually insensitive to manufacturing process variations.
2. Description of the Prior Art
Vibrating beam force sensing elements used as resonators in crystal-controlled oscillators are generally known in the art. Examples of such force sensing elements are disclosed in U.S. Pat. Nos. 4,215,570; 4,372,173; 4,415,827; 4,901,586 and 4,912,990. Such force sensing elements have been known to be used in various transducers to measure various parameters, including acceleration, force, temperature, pressure and weight. In particular, such vibrating beam force sensing elements are responsive to forces, such as axial forces, which cause a variation of the frequency of vibration of the beams which, in turn, causes a variation in the output frequency of the oscillator which, in turn, can be used as a measure of the applied force.
An important consideration in transducers having vibrating beam force sensing elements is the mechanical Q of the element. The mechanical Q is the ratio of the energy stored to the energy lost in the vibrating beams for each cycle of vibration. A force sensing element with a relatively low mechanical Q will result in increased power requirements for the oscillator and can result in relatively unstable oscillations. The frequency of oscillation is also more sensitive to changes in the oscillator electronics and ambient conditions in low Q systems. For these reasons, it is desirable to optimize the mechanical Q of the force sensing element.
However, the mechanical Q of such force sensing elements tends to be sensitive to manufacturing process variations as well as other factors, including a phenomenon known as end pumping. End pumping relates to a condition in which a portion of the energy in the vibrating beams is transferred to the transducer mounting structure (e.g., ground connection) and is thereby lost. More particularly, such vibrating beam force sensing elements include generally parallel, spaced-apart beams connected together at opposite ends to form end portions. The force sensing element is then disposed within a transducer with one end portion rigidly secured to a stationary ground connection or mounting structure and the other end portion is rigidly secured to a movable structure, such as a proof mass. End pumping causes the transfer of energy from the vibrating beams to the mounting structure in the transducer housing.
The end pumping phenomenon is best understood with reference to a single beam force sensing element as illustrated in FIG. 1. In particular, vibration of the beam results in a moment at the end portion due to reaction forces counteracting the turn around acceleration of the beam element. This results in finite motion at the ground connection that causes energy to be transferred from the resonant beam into the ground connection. As a result, the mechanical Q of the force sensing element is reduced. Additionally, if the ground connection is reactive in its response to the transferred energy, it can interact with the resonance and cause localized non-linearities in the force-to-frequency function, commonly called "activity dips". Such activity dips typically occur when the coupled resonance in the mounting frame structure falls within the operating frequency range of the vibrating beam force sensing element. In order to solve this problem with single beam force sensing elements, elaborate schemes have been developed to provide active dynamic counterbalancing mechanical isolators. However, even though such mechanical isolators have been found to be effective, they substantially add to the size, cost, complexity and axial compliance of the force sensing element; all of which are undesirable.
Two-beam force sensing elements as illustrated in FIG. 2 have also been utilized to reduce reaction forces to ground through the process of cancellation; however, even though the reaction forces to ground cancel in the two-beam force sensing elements, there are other problems. More specifically, in such force sensing elements, the end portions are used to couple the vibrating beams such that they vibrate in sympathetic motion at the same frequency, but 180.degree. out of phase with respect to each other. Even though such two-beam force sensing elements do not require mechanical isolators to achieve relatively high mechanical Q's, the vibrating beams must be closely coupled in order for the two-beam system to resonate at a single frequency. This requires the force sensing element to be formed such that the beams are relatively close together. However, this can lower the mechanical Q of the force sensing element when it is operated in a gas. More particularly, in such a situation, the gas is pumped into and out of the gap between the vibrating beams forming a squeeze film gas damper which effectively lowers the mechanical Q.
In order to solve the various problems associated with the above-mentioned force sensing elements, a three-beam force sensing element as illustrated in FIG. 3 evolved to cancel reaction forces to ground. In a three-beam force sensing element, the outer beams move out of plane and in phase with each other, but 180.degree. out of phase with the center beam. In order to provide dynamic balance, the center beam must have approximately twice the mass of the outer beams. A principal advantage of the three-beam force sensing element is that the gas damping between the tines is driven only by a shearing motion which generates an order of magnitude less damping than the compressive-expansive squeeze film damping produced by the two-beam force sensing element discussed above. However, there are various disadvantages of a three-beam force sensing element, including the added complexity of the center beam; the bending strength profile in the end portions, which is more difficult to localize and isolate; and the difficulty in creating precisely mass balanced beams. The mass balancing problem is further aggravated by the different widths of the beams. In particular, when the beams are fabricated, variations in the processing can affect the width of the beams. Because the center beam is approximately twice the width of the outer beams, a processing variation which affects the width of the beams will have twice the effect on mass variations on the outer beams as it has on the center beams. As such, mass balancing is extremely process sensitive.